Emergence of electric-field-tunable interfacial ferromagnetism in 2D antiferromagnet heterostructures

Van der Waals (vdW) magnet heterostructures have emerged as new platforms to explore exotic magnetic orders and quantum phenomena. Here, we study heterostructures of layered antiferromagnets, CrI3 and CrCl3, with perpendicular and in-plane magnetic anisotropy, respectively. Using magneto-optical Kerr effect microscopy, we demonstrate out-of-plane magnetic order in the CrCl3 layer proximal to CrI3, with ferromagnetic interfacial coupling between the two. Such an interlayer exchange field leads to higher critical temperature than that of either CrI3 or CrCl3 alone. We further demonstrate significant electric-field control of the coercivity, attributed to the naturally broken structural inversion symmetry of the heterostructure allowing unprecedented direct coupling between electric field and interfacial magnetism. These findings illustrate the opportunity to explore exotic magnetic phases and engineer spintronic devices in vdW heterostructures.

controlled magnetism in 2L CrI3 5 . In contrast, we observed an extra FM-type transition near zero field in addition to the high field induced spin-flip transitions for the 2L CrI3/FL CrCl3 heterostructures (Supplementary Fig. 6 and Fig. 1d), which is consistent with our proposed scenario where at least three spin layers (two layers of CrI3 plus one neighboring layer of CrCl3) are responsible for the observations, and is qualitatively different from the symmetry-breaking induced effect (Supplementary Fig. 6).
(b) Bubble-induced strain. Bubbles generally could exist in 2D heterostructures and the bubble-induced local strain may modulate the magnetism 4 . The AFM images of typical heterostructures suggest uniform interfaces with few bubbles (Supplementary Fig. 7a,b). During the MOKE measurement, we also intentionally parked the laser spot away from the visible deformations (e.g., bubbles, wrinkles) under the microscope ( Supplementary Fig. 7c). In contrast to the random distribution of the bubbles, the emergent FM loop is well reproduced in almost all the heterostructure samples (summarized in Supplementary Fig. 8).
Moreover, bubbles could also exist in other 2D stacks, but we have never observed anomalous features (e.g., the FM loop) in BN/2L CrI3/BN, including 2L CrI3 regions in the heterostructure samples or pure 2L CrI3 samples. Even if bubble-induced strain plays a role, the strain is reported to just modulate the magnetic interactions (changing the transition field) in 2L CrI3 4 , different from the emergent FM loop in 2L CrI3/FL CrCl3 heterostructure. Therefore, it is unlikely that the bubble-induced strain plays an important role in our work.
(c) Surface-related magnetism. The surface-related magnetism may modulate the magnetic order. For example, it is reported that FM-like magnetic loops are observed in all even-number septuple-layered (SL) MnBi2Te4-including 2L MnBi2Te4-which is attributed to the "surfacerelated magnetism" of unknown origin 7 . In contrast, first we note that, in 2L CrI3 region with the same top surface as 2L CrI3/FL CrCl3, we did not observe the emergent FM loop. This strongly suggests that our observations originate from the interfacial CrCl3. We also studied reversely stacked heterostructures with FL CrCl3 on top of 2L CrI3 and observed similar FM loops (Supplementary Fig. 2) (while such FM loops are again absent in the exposed 2L CrI3 region or FL CrCl3 region on the same sample), which further lends support to the role of interfacial CrCl3 proximal to CrI3.
When forming an interface with CrCl3, CrI3 may be affected by the adjacent CrCl3. However, it is well-established that the magnetic state in CrCl3 is more susceptible as opposed to that in CrI3. This is because CrCl3 is located close to the boundary between perpendicular magnetic anisotropy (PMA) and in-plane anisotropy 8,9 . Consistent with this, based on the DFT calculations presented in our original manuscript, we find that the interfacial FM exchange coupling in the heterostructure wins over the in-plane anisotropy of CrCl3 and results in the out-of-plane magnetic order in the CrCl3 layer next to CrI3, in agreement with our observations. Furthermore, we also do not believe disorders or surface impurities-related magnetism is the likely scenario because they usually lower the critical temperatures (TC) 10,11 . While for the heterostructure, we observed enhanced TC. As shown in Fig. 2 and Supplementary Fig. 5, TC of the FM-like hysteresis loop in the 2L CrI3/FL CrCl3 heterostructure (~48 K) is higher than that of either 2L CrI3 (~40 K) and FL CrCl3 (~18.6 K). Another experiment ( Supplementary Fig. 4) on 1L CrI3/FL CrCl3 heterostructure shows TC of ~ 33 K and ~ 37 K for 1L CrI3 and the 1L CrI3/FL CrCl3 heterostructure, respectively. The enhanced TC can be understood by the effective anisotropy field deriving from the interfacial ferromagnetic coupling in the heterostructure, which is expected to enlarge the spin-wave gaps for the adjacent magnetic materials [12][13][14] .
Overall, the surface-related magnetism is thus also less likely to be an important mechanism explaining the experimental observations in our samples.

First-principles perspectives of the CrI3/CrCl3 heterostructures
DFT simulation is widely implemented to predict the magnetic properties of both monolayers 15,16 and homobilayers 17,18 . In this section, we demonstrate the results from our DFT calculations using the Vienna ab-initio Simulation Package (VASP) 19 to support the observed out-of-plane magnetic order as well as the interfacial ferromagnetic coupling in CrI3/CrCl3 heterostructures.

5.93Å×7
× 100% ≈ 1.4% ). As suggested in ref. 18 , we employed PBEsol 20 functional throughout our calculations. We also used a 3×3×1 Monkhorst-Pack k-point grid and chose the plane-wave energy cutoff of 300 eV 21 . We checked with other grid sizes and a higher energy cutoff of 400 eV, and the results indicate that our conclusion of interfacial ferromagnetic coupling is unaffected. Since the results of previous literature 22 show that magnetic configurations have little influence on the lattice structure of CrX3 (X = I, Cl), we can relax the structure in one magnetic state and use the optimized structure throughout. Following ref. 18 and ref. 16 , the structure was fully relaxed within a perpendicular ferromagnetic state (both intralayer and interlayer). The force convergence criterion was set to 30 meV/Å. In anisotropic magnetism calculations, we employed DFT+U method introduced by Liechtenstein et al. 23 to deal with strong correlations of Cr-3d electrons. We set effective on-site Coulomb interaction U=3 eV and Hund's rule coupling JH=0 eV according to the benchmark calculations in a previous study 24 . Spin-orbit coupling (SOC) was included in all magnetic configuration calculations.
Twisting one CrI3 layer relative to another layer with a small angle may lead to alternating stacking domains and non-collinear AFM-FM domains with sufficiently large moiré periodicity (typically ≳ 10 nm for twisted CrI3 18,25,26 ). For the CrI3/CrCl3 heterostructure, with a large lattice constant mismatch (6.82 Å and 5.93 Å for CrI3 and CrCl3, respectively 18 ), our random stacking typically results in large twist angles and small nominal moiré periodicity (~4.5 nm for 0˚, ~1 nm for 30˚, calculated following Ref. 27 ). For such small moiré periodicity, the energy cost of forming magnetic domain walls becomes too high that the system eventually collapses to a collinear phase with no domains 25,26 . Therefore, instead of having moiré -related magnetic domains in the heterostructure, we consider an averaged magnetic moment in each magnetic layer.
We denote spins in each layer by a macroscopic spin (out-of-plane: ↑, ↓; in-plane: ←, →). In our calculations, we studied four types of magnetic configurations: perpendicular ferromagnetic state (↑↑), perpendicular antiferromagnetic state (↑↓), the state that CrI3 is out-of-plane polarized while CrCl3 in-plane polarized (↑→), and the state that CrI3 is in-plane polarized while CrCl3 outof-plane polarized (→↑). The ground-state energies of the supercells are denoted as FM , AFM , Next, we proceed to make a quantitative estimation of the induced parameters. To this end, within a continuum model of locally coupled spin densities, the magnetic energy of the system (normalized to per unit area of the supercell) can be written as 17, 18 where inter is the interlayer exchange energy in CrI3/CrCl3, |S1(2)|=3/2 is the spin for Cr atom 29  ≈293 μJ/m 2 @0˚, 287 μJ/m 2 @30˚, larger than that of the intrinsic CrI3 ~108 μJ/m 2 29 . Such higher anisotropy of CrI3 qualitatively agrees with the observed enhanced critical temperature (TC * >TC in Fig. 2).
The effective anisotropy of CrCl3 in the heterostructure 2 = in the out-of-plane magnetic order in CrCl3, as we observed in this work. in the presence of external magnetic fields (the so-called "magnetoelectric effect") 5 .

Analysis of the electric field tunability in
To understand the electric field tunability of the CrI3/CrCl3 heterostructure, we consider here a dual gated CrI3/CrCl3 system with 1 and 2 charges introduced to the corresponding layers via capacitive gates. Similar to Equation (S1), the free energy per unit area of such a system under the macroscopic approximation can be written as According to the Neumann's principle 34 , any physical property of the system must respect the system's inherent symmetries. We apply this principle to write down the spin-charge coupling Hamiltonian for heterobilayer system studied here (corresponding to CrCl3/CrI3) and compare it with the case of homobilayer of CrI3. Most importantly, the heterobilayer (homobilayer) crystal breaks (respects) the spatial inversion symmetry I 2 , which gives rise to spin-charge coupling terms in heterobilayers consistent with the experimental observations, as shown below. Moreover, we exploit the presence of time-reversal symmetry (i.e., when magnetization is allowed to transform) and assume continuous spin rotations ( ) about the z-axis (oriented along the normal to the 2D magnet plane) as an additional symmetry to restrict the form of spin-charge coupling terms. We remark here that assuming amounts to neglecting the presence of a special crystal axis in the xy plane of the system. In principle, this assumption can be relaxed to write more general terms, such as charge-controlled in-plane magnetic anisotropies. However, in this work we do not focus on such terms for the following reasons: (i) in-plane magnetic anisotropies, even in pristine chromium halides of interest here, have been found to be parametrically smaller than out-of-plane anisotropies 16,29,35 ; we thus expect the charge control of out-of-plane anisotropies to play a more dominant role, (ii) the spin-charge coupling we study here is observed in randomly stacked largeangle twisted structures, which further suggests the in-plane crystal structure does not play a major Here, in the spirit of linear response, we only keep terms which are linear in , while including terms up to the second order in (to capture magnetic anisotropies and interlayer exchange); the superscript on the right-hand side indicates the order of the term with respect to . The zeroth-order terms correspond to a constant reference and thus do not contribute to spincharge coupling. Next, we will enumerate possible first-and second-order terms and only keep the ones that respect the symmetries of the system to arrive at the spin-charge coupling Hamiltonian.
For the second-order terms, we can write them as: Thus, the electric-field induced spin-charge coupling terms that are only allowed in heterobilayers (but not in homobilayers) can be succinctly written as the electric-field-dependent perpendicular anisotropy and interlayer exchange (which is the equation used in the main manuscript): (2) = − ( 1 1 2 + 2 2 2 + 3 1 • 2 ). (S10) Here, for simplifying notations, we have redefined the variables: Therefore, breaking the structural inversion symmetry by choosing two different layers for the heterostructure allows for spin-charge coupling terms which can couple directly to electric fields. These terms can be written as elec ( , ) = ( 1 − 2 )( 1 1 2 + 2 2 2 + 3 1 ⋅ 2 ), and can be understood as electric field control of magnetic anisotropy (ECMA) and interlayer exchange (ECIJ), respectively, where 1,2,3 parameterizes the strength of such interactions. In particular, since the coercivity is predominantly controlled by magnetic anisotropy, the observed electric field control of coercivity in Fig. 3c,e seems consistent with the predicted ECMA terms.

Electric control of the magnetism in FL CrCl3/2L CrI3 heterostructure
The intriguing electrical tunability allowed by symmetry breaking is also observed in a heterostructure containing a bilayer CrI3. Supplementary Fig. 11a,b shows the optical micrograph and schematic structure of a reversely stacked FL CrCl3/2L CrI3 device. Supplementary Fig. 11c,d presents θK as a function of both Vbg and perpendicular magnetic field in 2L CrI3 and the heterostructure, respectively (see representative MOKE curves in Supplementary Fig. 3). Similar to the heterostructure in Fig. 1, we also observed the antiferromagnetic spin-flip transitions in 2L CrI3 and the ferromagnetic coercivity in the FL CrCl3/2L CrI3 heterostructure (dashed lines in Supplementary Fig. 11d). In 2L CrI3, the critical field of antiferromagnetic spin-flip shrinks with increasing Vbg. This observation is consistent with the previous reports 6, 31 and derives from the effective tuning of the interlayer exchange interaction by electrostatic doping effect instead of the displacement field.
In the heterostructure, the electrical control of critical field of the antiferromagnetic spin-flip weakens, presumably due to the doped-charge redistribution to the contacting CrCl3 layer.
Remarkably, the interfacial ferromagnetism is highly controllable by electrostatic gating.